Fractional integration, stable distributions and long-memory models of foreign exchange rates

by Assaf, Ata A.

A major issue in financial economics is the behavior of asset retums over long horizon as oppowd to short horizons. This study provides empirical evidence fkom the perspective of long memory analysis. Evidence of long memory is éxplored using international currency prices for fourteen countries. The measure of long-term persistence employed is the modified rescaled range statistic proposed by Lo (1991),which tests for longrange dependence aRer having accounted for a wide range of short-memory processes. F'urther analpis is conducted on the squared and absolute returns of the series, using the procedure proposed by Geweke and Porter- Hudak (1983). The empirical rdts provide strong nippon for long memory in international currency retum,-squared returns and absolute retums. Most of the d estimates fa11 in the range of (0,1/2), a characteristic of the hyperbolic decay of the autocorrelation function of ARFIMA models in their ability of capturing the long memory property. These findings suggest that models of exchange rate should be made to accommodate the long memory in the conditional mean and variance of the returns. A related issue is the performance in hite samplesof the dinerent tests and estimators under Stable-ARFIMA process. Using Monte Car10 simulations, it is found that the traditional and modified R/S behaves in a similor fashion. Different estimators of the long-rnemory parameter are then compared for processes with stable errors. L'analyse du cornportment des rendements au long terme contrairement court terme constitute un grand problème en économie hancière. Cette étude fournit une évidence empirique du point de vue du long terme. Cette évidence est explor& à travers les prix de quatorze devises internationales. La mesure de la persistence au long terme est le R/S moàifié, proposé par Lo (1991), et qui teste la dépendence au long-term aprés avoir reconnu un grand nombre de courts processus de mémoire. En outre, l'analyse porte sure les rendements absolus et carrés des series utilisant la procédure proposée par Geweke et Porter-Hudak (1983). Les résultats empiriques fournissent un long support pour la longue mémoire en rendements de devises intemationaes ainsi qu'aux rendements carrés et absolus. La plupart des estimations d sont comprises dans l'intervale (0,112) ce qui caractérise! la chute hyperbolique de la fonction de I'autocorrelation des modèls ARFW dans leur abilité de capturer la propriété de longue mémoire. Les résultats suggestent que les modéls de taux de change doivent accomoder la long mémoire dans la moyenne conàitionelle et la variance des rendements. La performance des échantillons finis des difiérents tests et estimateurs sous le processus Stable ARFIMA est un autre sujet traité. En utilisant tes simulations Monte Cario, on a trouvé que le R/Straditionnel et modifié se comportent de la même manière. Les différents estimateurs du paramétre de longue mémoire sont comparés aux processus avec des erreurs stables. There are many individuais who played an important rob in the production of this thesis. First and foremost, 1 wouid like to thank the people from whom 1 learnt much of what 1 know about econometrics and empirical analysis. 1owe a great academic debt to my principal supervisors, professors John W. Galbraith and Victoria Zinde-\Vaish. Both have been very generous with their time and advice, and large parts of tbis thesis are based on their constant and unconditional support. 1am grateful to both of them for their many suggestions and comments, and their constant encouragement. An empirical work such as this one would not have been possible without the availability of - econornic data series. Professor John McCdum, currently the chief economist at Royal Bank of Canada has made it easier for me by providing me with ail the data needed for my research. 1 me a great deal to bis support and generosity. I am also gratefd to all the professors at the Economics Department, who taught me ail the way long through my graduate studies. Many other people in the department have provided always their support and help, in particdar, I would like to eupress my sincere thanks to al1 the staff working , mnking sure I have my work completed on time. Last, but not least, 1am gratefd to my parents who always provided me with their unconditional support and encouragement, and al1 my friends wbo made sure all the times, that 1 have the cornfort and tirne to continue my research.